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Measuring the strangeness of strange attractors. (English) Zbl 0593.58024

The authors consider the question of which observables may be effectively used to distinguish chaos and random noise in a dynamical system possessing a strange attractor. After briefly reviewing some such quantities (fractal dimension, Lyapunov exponents information entropy), the authors suggest another such measure, the correlation exponent. This exponent is closely related to the above quantities, but its computation is considerably easier. The authors then describe this exponent in a variety of examples.
Reviewer: R.Devaney

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
28A80 Fractals
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
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